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Concyclic Points

Source: Turkey TST 2013 - Day 3 - P1

April 2, 2013
geometrycircumcirclegeometry proposed

Problem Statement

Let EE be intersection of the diagonals of convex quadrilateral ABCDABCD. It is given that m(EDC^)=m(DEC^)=m(BAD^)m(\widehat{EDC}) = m(\widehat{DEC})=m(\widehat{BAD}). If FF is a point on [BC][BC] such that m(BAF^)+m(EBF^)=m(BFE^)m(\widehat{BAF}) + m(\widehat{EBF})=m(\widehat{BFE}), show that AA, BB, FF, DD are concyclic.
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